ion-g-ion / tt-iga

Isogeometric Analysis Finite Element Method using Tensor Trains

TT-IGA

This repository contains the code for the paper "Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries".

Installation

Requirements

For using just the TT-IGA package:

• pytorch>=1.7
• numpy>=1.18
• scipy
• torchtt
• opt_einsum
• matplotlib
• pandas
• scipy

Optional dependencies to run the reference FEM solver are:

• fenics

Using pip

You can install the package using the following pip command:

pip install git+https://github.com/ion-g-ion/code-paper-tt-iga

Packages

Scripts and examples:

• convergence_one_param.py: Convergence study (Test case 1).
• Cshape_study.py: Increasing the number of parameters (Test case 2).
• material_jump.py / material_jump.ipynb: Laplace equation in a cylinder with material filling -> Open using Google Colab.
• material_jump_study.py / material_jump_study.ipynb: Laplace equation in a cylinder with material filling (Test case 3: tables).
• waveguide.py / waveguide.ipynb: Helmholtz equation inside a waveguide (Test case 4) -> Open using Google Colab.
• twisted.py / twisted.ipynb: Example of a twisted cylinder -> Open using Google Colab.

The documentation is generated using pdoc3 with:

pdoc3 --html tt_iga -o docs/ --config latex_math=True --force

Author

Ion Gabriel Ion, [e-mail]